Robust Stability Analysis of an Optical Parametric Amplifier Quantum System

TL;DR

This paper develops a robust stability criterion for uncertain nonlinear quantum systems, specifically applied to an optical parametric amplifier, extending previous results to include non-quadratic Hamiltonian perturbations.

Contribution

It introduces a new stability condition for nonlinear quantum systems with non-quadratic Hamiltonian perturbations, broadening the scope of robust quantum system analysis.

Findings

Derived a strict bounded real condition for stability

Extended stability analysis to non-quadratic Hamiltonian perturbations

Applied the results to an optical parametric amplifier model

Abstract

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic perturbations to the system Hamiltonian. The paper extends recent results on the robust stability of nonlinear quantum systems to allow for non-quadratic perturbations to the Hamiltonian which depend on multiple parameters. A robust stability condition is given in terms of a strict bounded real condition. This result is then applied to the robust stability analysis of a nonlinear quantum system which is a model of an optical parametric amplifier.